To solve the equation (3x - 8) x 5 = 5^3, we can follow these steps:

1. Simplify the left side of the equation:
(3x - 8) x 5 = 5^3
15x - 40 = 125

2. Add 40 to both sides of the equation to isolate the variable:
15x - 40 + 40 = 125 + 40
15x = 165

3. Divide both sides of the equation by 15 to solve for x:
15x/15 = 165/15
x = 11

Therefore, the solution to the equation is x = 11.